Finite Group Databasebeta

← #6467283

Subgroups — #6467283

Order 512.

1956 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2967C211yesmaximal, characteristic
2C2×#2950C211yesmaximal, characteristic, complemented
3#35663C212yesmaximal
4#28274C211yesmaximal, characteristic, complemented
5#28271C211yesmaximal, characteristic, complemented
6#28234C211yesmaximal, characteristic, complemented
7#28232C211yesmaximal, characteristic, complemented
8#28198C212yesmaximal, complemented
9#28153C212yesmaximal, complemented
10#28112C212yesmaximal, complemented
11#28102C212yesmaximal, complemented
12#27665C211yesmaximal, characteristic, complemented
13#27665C211yesmaximal, characteristic, complemented
14#24273C211yesmaximal, characteristic, complemented
15#24273C211yesmaximal, characteristic, complemented
16#23713C212yesmaximal, complemented
17#23709C212yesmaximal, complemented
18#21537C211yesmaximal, characteristic, complemented
19#21537C211yesmaximal, characteristic, complemented
20C4×#470C211yesmaximal, characteristic, complemented
21C4×#470C211yesmaximal, characteristic, complemented
22#20820C211yesmaximal, characteristic, complemented
23#20745C212yesmaximal, complemented
24C23×Q16C2211yescharacteristic
25C2×#529C2211yescharacteristic
26C2×#519C2212yes—
27C2×#470C2211yescharacteristic
28C2×#470C2211yescharacteristic
29C2×#470C2211yescharacteristic
30C2×#470C2211yescharacteristic
31#2967—28no—
32C2×#446C2211yescharacteristic
33C2×#446C2211yescharacteristic
34#2950—28no—
35C2×#441C2212yes—
36C2×#441C2212yes—
37C2×C4×Q16C2211yescharacteristic
38C2×C4×Q16C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41C2×#436C2211yescharacteristic
42C2×#436C2211yescharacteristic
43C2×#435C2211yescharacteristic
44C2×#435C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#435C2211yescharacteristic
47C2×#433C2211yescharacteristic
48C2×#433C2211yescharacteristic
49C2×#432C2211yescharacteristic
50C2×#427C2211yescharacteristic
51C2×#419C2212yes—
52C2×#405C2211yescharacteristic
53C2×#405C2211yescharacteristic
54C2×C4×M16C2211yescharacteristic
55#2582C2212yes—
56#2581C2212yes—
57#2538C2212yes—
58#2536C2212yes—
59#2485C2212yes—
60#2485C2212yes—
61#2478—22no—
62#2476—22no—
63#2474—22no—
64#2470—22no—
65#2469—22no—
66#2465—22no—
67#2462—22no—
68#2458—22no—
69#2409C2212yes—
70#2409C2212yes—
71#2323C2212yes—
72#2323C2212yes—
73#2314C2212yes—
74C4×C22⋊Q8C2212yes—
75C4×C22⋊Q8C2212yes—
76#2088C2212yes—
77#2088C2212yes—
78#2077C2212yes—
79#2077C2212yes—
80#2068C2212yes—
81#2068C2212yes—
82#2066C2212yes—
83#2066C2212yes—
84#2056C2212yes—
85#2056C2212yes—
86#2036C2212yes—
87#2036C2212yes—
88#2035C2212yes—
89#2035C2212yes—
90#2001C2212yes—
91#2001C2212yes—
92#1971C2211yescharacteristic
93#1971C2211yescharacteristic
94#1971C2211yescharacteristic
95#1971C2211yescharacteristic
96#1944C2211yescharacteristic
97#1944C2211yescharacteristic
98#1944C2211yescharacteristic
99#1944C2211yescharacteristic
100#1935C2212yes—
101#1935C2212yes—
102#1933C2212yes—
103#1933C2212yes—
104#1894C2212yes—
105#1894C2212yes—
106#1892C2212yes—
107#1892C2212yes—
108#1846C2211yescharacteristic
109#1844C2211yescharacteristic
110#1836C2212yes—
111#1825C2212yes—
112#1825C2212yes—
113#1809C2211yescharacteristic
114#1809C2211yescharacteristic
115#1809C2211yescharacteristic
116#1809C2211yescharacteristic
117#1809C2212yes—
118#1807C2211yescharacteristic
119#1807C2211yescharacteristic
120#1805C2212yes—
121#1805C2212yes—
122#1803C2212yes—
123#1803C2212yes—
124#1787C2212yes—
125#1787C2212yes—
126#1776C2212yes—
127C4×#106C2211yescharacteristic
128C4×#106C2211yescharacteristic
129#1763C2212yes—
130#1763C2212yes—
131C4×#103C2212yes—
132C4×#103C2212yes—
133C23×Q8C2312yes—
134C22×Q16—24no—
135C22×Q16—24no—
136C22×Q16—24no—
137C22×Q16C2312yes—
138C22×Q16C2311yescharacteristic
139C22×Q16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C22×M16C2311yescharacteristic
142C22×M16C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146#529—24no—
147#529—24no—
148C2×#126D411yescharacteristic
149C2×#126D411yescharacteristic
150C2×#125D411yescharacteristic
151C2×#124D411yescharacteristic
152C2×#123D411yescharacteristic
153C2×#123D411yescharacteristic
154C2×C22⋊Q8D411yescharacteristic
155C2×C22⋊Q8C2312yes—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×#121D411yescharacteristic
160#519—28no—
161#519—28no—
162C2×C4×Q8—22no—
163C2×C4×Q8—22no—
164C2×C4×Q8C2312yes—
165C2×C4×Q8C2312yes—
166C2×C4×Q8C2312yes—
167C2×C4×Q8C2312yes—
168C2×C4×Q8C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2311yescharacteristic
172C2×#117—22no—
173C2×#117—22no—
174C2×#117C2312yes—
175C2×#117C2311yescharacteristic
176C2×#117C2311yescharacteristic
177C22×C42C2311yescharacteristic
178#470—24no—
179#470—24no—
180#470—24no—
181#470—24no—
182#446—24no—
183#446—24no—
184#441—28no—
185#441—28no—
186C4×Q16—24no—
187C4×Q16—24no—
188C4×Q16—24no—
189C4×Q16—24no—
190#436—24no—
191#436—24no—
192#435—24no—
193#435—24no—
194#435—24no—
195#435—24no—
196#433—24no—
197#433—24no—
198#432—24no—
199#427—24no—
200C2×#107C2311yescharacteristic
201C2×#107C2311yescharacteristic
202C2×#107C2312yes—
203C2×#106C2311yescharacteristic
204C2×#106C2311yescharacteristic
205C2×#106C2311yescharacteristic
206C2×#106C2311yescharacteristic
207C2×#106C2312yes—
208C2×#106C2312yes—
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2311yescharacteristic
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2311yescharacteristic
214C2×C4⋊C8C2311yescharacteristic
215#419—28no—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#103C2312yes—
224C2×#103C2312yes—
225C2×#103C2312yes—
226C2×#103C2312yes—
227C2×#103C2312yes—
228C2×C22⋊C8C2311yescharacteristic
229C2×C22⋊C8C2311yescharacteristic
230C2×C22⋊C8C2311yescharacteristic
231C2×C22⋊C8C2311yescharacteristic
232C2×C22⋊C8C2311yescharacteristic
233C2×C22⋊C8C2311yescharacteristic
234#405—24no—
235#405D418yes—
236C4×M16—24no—
237C2×#97C2311yescharacteristic
238C2×#97C2311yescharacteristic
239C2×#97C2311yescharacteristic
240C2×#97C2311yescharacteristic
241C2×#97C2311yescharacteristic
242C2×#97C2311yescharacteristic
243C2×C4×C8C2311yescharacteristic
244C2×C4×C8C2311yescharacteristic
245C2×C4×C8C2311yescharacteristic
246C2×C4×C8C2311yescharacteristic
247#400—22no—
248#398—22no—
249#398—22no—
250#398—22no—
251#397—22no—
252#397—22no—
253#396—22no—
254#396—22no—
255#395—22no—
256#395—22no—
257#395—22no—
258#394—22no—
259#394—22no—
260#394—22no—
261#393—22no—
262#393—22no—
263#391—22no—
264#391C2312yes—
265#391C2312yes—
266#391C2312yes—
267#391C2312yes—
268#390—22no—
269#389—22no—
270#389—22no—
271#389—22no—
272#389—22no—
273#389C2312yes—
274#389C2312yes—
275#389C2312yes—
276#389C2312yes—
277#388—22no—
278#388—22no—
279#388—22no—
280#388—22no—
281#388—22no—
282#388—22no—
283#388—22no—
284#388—22no—
285#388—22no—
286#388—22no—
287#387—22no—
288#387—22no—
289#387—22no—
290#387—22no—
291#387—22no—
292#387—22no—
293#387—22no—
294#387—22no—
295#387—22no—
296#387—22no—
297#386—22no—
298#386—22no—
299#385—22no—
300#385—22no—
301#385—22no—
302#385—22no—
303#384C2312yes—
304#382C2312yes—
305#380C2312yes—
306#380C2312yes—
307#380C2312yes—
308#380C2312yes—
309#380C2312yes—
310#380C2312yes—
311C4×C4⋊C4—22no—
312C4×C4⋊C4—22no—
313C4×C4⋊C4C2312yes—
314C4×C4⋊C4C2312yes—
315C4×C22⋊C4—22no—
316C4×C22⋊C4—22no—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329C22×Q8—22no—
330C22×Q8—24no—
331C22×Q8—24no—
332C22×Q8—24no—
333C22×Q8—24no—
334C22×Q8—42no—
335C22×Q8—42no—
336C22×Q8C2×D411yescharacteristic
337C22×Q8C2412yes—
338C22×Q8C2412yes—
339C22×D4C2×D411yescharacteristic
340C22×D4C2×D411yescharacteristic
341C22×D4C2×D411yescharacteristic
342C23×C4—22no—
343C23×C4C2×D411yescharacteristic
344C23×C4C2×D411yescharacteristic
345C23×C4C2411yescharacteristic
346C23×C4C2411yescharacteristic
347C23×C4C2411yescharacteristic
348C2×Q16—232no—
349C2×Q16—24no—
350C2×Q16—24no—
351C2×Q16—22no—
352C2×Q16—22no—
353C2×Q16—24no—
354C2×Q16—22no—
355C2×Q16—22no—
356C2×Q16#4114yes—
357C2×Q16#4114yes—
358C2×M16—22no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—41no—
366C2×M16—41no—
367C2×M16—41no—
368C2×M16—41no—
369C2×M16C2×D414yes—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—41no—
374C22×C8—41no—
375C22×C8C2×D414yes—
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2411yescharacteristic
379C22×C8C2411yescharacteristic
380C22×C8C2411yescharacteristic
381C22×C8C2411yescharacteristic
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384#126—24no—
385#126—24no—
386#125—24no—
387#124—24no—
388#123—24no—
389#123—24no—
390C22⋊Q8—24no—
391C22⋊Q8—24no—
392C22⋊Q8—24no—
393C22⋊Q8—24no—
394C22⋊Q8—24no—
395C22⋊Q8—42no—
396C22⋊Q8—42no—
397C22⋊Q8—42no—
398C22⋊Q8—42no—
399#121—24no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—24no—
403C4×Q8—24no—
404C4×Q8—24no—
405C4×Q8—24no—
406C4×Q8—24no—
407C4×Q8—24no—
408C4×Q8—24no—
409C4×Q8—24no—
410C4×Q8—48no—
411C4×Q8—48no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418#117—22no—
419#117—22no—
420#117—24no—
421#117—24no—
422#117—48no—
423#117—48no—
424#117C2×D414yes—
425#117#4114yes—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2×D411yescharacteristic
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2412yes—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D411yescharacteristic
470C2×C22⋊C4C2×D411yescharacteristic
471C2×C22⋊C4C2×D411yescharacteristic
472C2×C22⋊C4C2×D411yescharacteristic
473C2×C22⋊C4C2×D411yescharacteristic
474C2×C22⋊C4C2×D411yescharacteristic
475C2×C22⋊C4C2×D411yescharacteristic
476C2×C22⋊C4C2×D411yescharacteristic
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492#107—22no—
493#107—22no—
494#107—42no—
495#106—24no—
496#106—22no—
497#106—22no—
498#106—22no—
499#106—22no—
500#106—42no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—24no—
511#103—24no—
512#103—24no—
513#103—24no—
514#103—24no—
515#103—42no—
516#103—42no—
517#103—42no—
518#103—42no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—22no—
524C22⋊C8—22no—
525#97—22no—
526#97—22no—
527#97—22no—
528#97—22no—
529#97C2×D414yes—
530#97C2×D414yes—
531C4×C8—22no—
532C4×C8—22no—
533C4×C8C2×D414yes—
534C4×C8C2×D414yes—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557C24C22×D411yescharacteristic
558C24C22×D411yescharacteristic
559C24C22×D411yescharacteristic
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—216no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—42no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—48no—
576C2×Q8—48no—
577C2×Q8—48no—
578C2×Q8—44no—
579C2×Q8C2×#4114yes—
580C2×Q8C2×#4114yes—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D412yes—
630C22×C4C2×#4112yes—
631C22×C4C2511yescharacteristic
632Q16—216no—
633Q16—28no—
634Q16—28no—
635M16—44no—
636M16—44no—
637M16—44no—
638M16—44no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—28no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—44no—
659C2×C8C22×D412yes—
660C2×C8C22×D412yes—
661C2×C8C22×D412yes—
662C2×C8C22×D412yes—
663C2×C8C2×#4112yes—
664C2×C8C2×#4112yes—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4—82no—
699C4⋊C4#12114yes—
700C4⋊C4#12114yes—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4—82no—
716C22⋊C4—82no—
717C22⋊C4—82no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C22⋊C4#12114yes—
721C22⋊C4#12114yes—
722C42—22no—
723C42—22no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—44no—
729C42—44no—
730C42—44no—
731C42—44no—
732C42—44no—
733C42—82no—
734C42—82no—
735C42C22×D412yes—
736C42C22×D412yes—
737C42C2×#4112yes—
738C42C2×#4112yes—
739C23—22no—
740C23—22no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23C2×#12112yes—
754C23C23×D411yescharacteristic
755Q8—24no—
756Q8—24no—
757Q8—24no—
758Q8—24no—
759Q8—416no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—82no—
765D4—82no—
766D4—82no—
767D4—82no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—416no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—82no—
826C2×C4—82no—
827C2×C4C2×#12112yes—
828C2×C4C2×#12112yes—
829C2×C4C2×#12112yes—
830C2×C4C2×#12112yes—
831C2×C4C2×#12112yes—
832C2×C4C23×D411yescharacteristic
833C2×C4C22×#4111yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C22×#4111yescharacteristic
836C2×C4#58511yescharacteristic
837C2×C4#58511yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8#52514yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22C22×#12111yescharacteristic
862C22D4×#4111yescharacteristic
863C22D4×#4111yescharacteristic
864C22#358612yes—
865C22#358612yes—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—44no—
878C4—44no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4C2×#52511yescharacteristic
886C4#344911yescharacteristic
887C4#347511yescharacteristic
888C4#347511yescharacteristic
889C2—42no—
890C2—81no—
891C2—81no—
892C2#3493511yescharacteristic
893C2#6046211yescharacteristic
894C2#6046211yescharacteristic
895C2#6151112yes—
896C2#6151212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2950C2semidirect
4. #28274C2semidirect
5. #28271C2semidirect
6. #28234C2semidirect
7. #28232C2semidirect
8. #28198C2semidirect
9. #28153C2semidirect
10. #28112C2semidirect
11. #28102C2semidirect
12. #27665C2semidirect
13. #27665C2semidirect
14. #24273C2semidirect
15. #24273C2semidirect
16. #23713C2semidirect
17. #23709C2semidirect
18. #21537C2semidirect
19. #21537C2semidirect
20. C4×#470C2semidirect
21. C4×#470C2semidirect
22. #20820C2semidirect
23. #20745C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#29672
C2×#29502
#356632
#282742
#282712
#282342
#282322
#281982
#281532
#281122
#281022
#276652
#242732
#237132
#237092
#215372
C4×#4702
#208202
#207452